spatstat.corepackage  R Documentation 
The spatstat.core package belongs to the spatstat family of packages. It contains the core functionality for statistical analysis and modelling of spatial data.
spatstat is a family of R packages for the statistical analysis of spatial data. Its main focus is the analysis of spatial patterns of points in twodimensional space.
The original spatstat package has now been split into several subpackages.
This subpackage spatstat.core contains all the main userlevel functions that perform statistical analysis and modelling of spatial data.
(The main exception is that functions for linear networks are in the separate subpackage spatstat.linnet.)
The orginal spatstat package grew to be very large. It has now been divided into several subpackages:
spatstat.utils containing basic utilities
spatstat.sparse containing linear algebra utilities
spatstat.data containing datasets
spatstat.geom containing geometrical objects and geometrical operations
spatstat.core containing the main functionality for statistical analysis and modelling of spatial data
spatstat.linnet containing functions for spatial data on a linear network
spatstat, which simply loads the other subpackages listed above, and provides documentation.
When you install spatstat, these subpackages are also
installed. Then if you load the spatstat package by typing
library(spatstat)
, the other subpackages listed above will
automatically be loaded or imported.
For an overview of all the functions available in
the subpackages of spatstat,
see the help file for "spatstatpackage"
in the spatstat package.
Additionally there are several extension packages:
spatstat.gui for interactive graphics
spatstat.local for local likelihood (including geographically weighted regression)
spatstat.Knet for additional, computationally efficient code for linear networks
spatstat.sphere (under development) for spatial data on a sphere, including spatial data on the earth's surface
The extension packages must be installed separately and loaded explicitly if needed. They also have separate documentation.
The spatstat family of packages is designed to support a complete statistical analysis of spatial data. It supports
creation, manipulation and plotting of point patterns;
exploratory data analysis;
spatial random sampling;
simulation of point process models;
parametric modelfitting;
nonparametric smoothing and regression;
formal inference (hypothesis tests, confidence intervals);
model diagnostics.
For an overview, see the help file for "spatstatpackage"
in the spatstat package.
Following is a list of the functionality provided in the spatstat.core package only.
To simulate a random point pattern:
Functions for generating random point patterns are now contained in the spatstat.random package.
To interrogate a point pattern:
density.ppp  kernel estimation of point pattern intensity 
densityHeat.ppp  diffusion kernel estimation of point pattern intensity 
Smooth.ppp  kernel smoothing of marks of point pattern 
sharpen.ppp  data sharpening 
Manipulation of pixel images:
An object of class "im"
represents a pixel image.
blur  apply Gaussian blur to image 
Smooth.im  apply Gaussian blur to image 
transect.im  line transect of image 
pixelcentres  extract centres of pixels 
rnoise  random pixel noise 
Line segment patterns
An object of class "psp"
represents a pattern of straight line
segments.
density.psp  kernel smoothing of line segments 
rpoisline  generate a realisation of the Poisson line process inside a window 
Tessellations
An object of class "tess"
represents a tessellation.
rpoislinetess  generate tessellation using Poisson line process 
Threedimensional point patterns
An object of class "pp3"
represents a threedimensional
point pattern in a rectangular box. The box is represented by
an object of class "box3"
.
runifpoint3  generate uniform random points in 3D 
rpoispp3  generate Poisson random points in 3D 
envelope.pp3  generate simulation envelopes for 3D pattern 
Multidimensional spacetime point patterns
An object of class "ppx"
represents a
point pattern in multidimensional space and/or time.
runifpointx  generate uniform random points 
rpoisppx  generate Poisson random points 
Classical exploratory tools:
clarkevans  Clark and Evans aggregation index 
fryplot  Fry plot 
miplot  Morisita Index plot 
Smoothing:
density.ppp  kernel smoothed density/intensity 
relrisk  kernel estimate of relative risk 
Smooth.ppp  spatial interpolation of marks 
bw.diggle  crossvalidated bandwidth selection
for density.ppp 
bw.ppl  likelihood crossvalidated bandwidth selection
for density.ppp 
bw.CvL  CronieVan Lieshout bandwidth selection for density estimation 
bw.scott  Scott's rule of thumb for density estimation 
bw.abram  Abramson's rule for adaptive bandwidths 
bw.relrisk  crossvalidated bandwidth selection
for relrisk 
bw.smoothppp  crossvalidated bandwidth selection
for Smooth.ppp 
bw.frac  bandwidth selection using window geometry 
bw.stoyan  Stoyan's rule of thumb for bandwidth
for pcf

Modern exploratory tools:
clusterset  AllardFraley feature detection 
nnclean  ByersRaftery feature detection 
sharpen.ppp  ChoiHall data sharpening 
rhohat  Kernel estimate of covariate effect 
rho2hat  Kernel estimate of effect of two covariates 
spatialcdf  Spatial cumulative distribution function 
roc  Receiver operating characteristic curve 
Summary statistics for a point pattern:
Fest  empty space function F 
Gest  nearest neighbour distribution function G 
Jest  Jfunction J = (1G)/(1F) 
Kest  Ripley's Kfunction 
Lest  Besag Lfunction 
Tstat  Third order Tfunction 
allstats  all four functions F, G, J, K 
pcf  pair correlation function 
Kinhom  K for inhomogeneous point patterns 
Linhom  L for inhomogeneous point patterns 
pcfinhom  pair correlation for inhomogeneous patterns 
Finhom  F for inhomogeneous point patterns 
Ginhom  G for inhomogeneous point patterns 
Jinhom  J for inhomogeneous point patterns 
localL  GetisFranklin neighbourhood density function 
localK  neighbourhood Kfunction 
localpcf  local pair correlation function 
localKinhom  local K for inhomogeneous point patterns 
localLinhom  local L for inhomogeneous point patterns 
localpcfinhom  local pair correlation for inhomogeneous patterns 
Ksector  Directional Kfunction 
Kscaled  locally scaled Kfunction 
Kest.fft  fast Kfunction using FFT for large datasets 
Kmeasure  reduced second moment measure 
envelope  simulation envelopes for a summary function 
varblock  variances and confidence intervals 
for a summary function  
lohboot  bootstrap for a summary function 
Related facilities:
plot.fv  plot a summary function 
eval.fv  evaluate any expression involving summary functions 
harmonise.fv  make functions compatible 
eval.fasp  evaluate any expression involving an array of functions 
with.fv  evaluate an expression for a summary function 
Smooth.fv  apply smoothing to a summary function 
deriv.fv  calculate derivative of a summary function 
pool.fv  pool several estimates of a summary function 
density.ppp  kernel smoothed density 
densityHeat.ppp  diffusion kernel smoothed density 
Smooth.ppp  spatial interpolation of marks 
relrisk  kernel estimate of relative risk 
sharpen.ppp  data sharpening 
rknn  theoretical distribution of nearest neighbour distance 
Summary statistics for a multitype point pattern:
A multitype point pattern is represented by an object X
of class "ppp"
such that marks(X)
is a factor.
relrisk  kernel estimation of relative risk 
scan.test  spatial scan test of elevated risk 
Gcross,Gdot,Gmulti  multitype nearest neighbour distributions G[i,j], G[i.] 
Kcross,Kdot, Kmulti  multitype Kfunctions K[i,j], K[i.] 
Lcross,Ldot  multitype Lfunctions L[i,j], L[i.] 
Jcross,Jdot,Jmulti  multitype Jfunctions J[i,j],J[i.] 
pcfcross  multitype pair correlation function g[i,j] 
pcfdot  multitype pair correlation function g[i.] 
pcfmulti  general pair correlation function 
markconnect  marked connection function p[i,j] 
alltypes  estimates of the above for all i,j pairs 
Iest  multitype Ifunction 
Kcross.inhom,Kdot.inhom 
inhomogeneous counterparts of Kcross , Kdot 
Lcross.inhom,Ldot.inhom 
inhomogeneous counterparts of Lcross , Ldot 
pcfcross.inhom,pcfdot.inhom 
inhomogeneous counterparts of pcfcross , pcfdot 
localKcross,localKdot 
local counterparts of Kcross , Kdot 
localLcross,localLdot 
local counterparts of Lcross , Ldot 
localKcross.inhom,localLcross.inhom 
local counterparts of Kcross.inhom , Lcross.inhom

Summary statistics for a marked point pattern:
A marked point pattern is represented by an object X
of class "ppp"
with a component X$marks
.
The entries in the vector X$marks
may be numeric, complex,
string or any other atomic type. For numeric marks, there are the
following functions:
markmean  smoothed local average of marks 
markvar  smoothed local variance of marks 
markcorr  mark correlation function 
markcrosscorr  mark crosscorrelation function 
markvario  mark variogram 
markmarkscatter  markmark scatterplot 
Kmark  markweighted K function 
Emark  mark independence diagnostic E(r) 
Vmark  mark independence diagnostic V(r) 
nnmean  nearest neighbour mean index 
nnvario  nearest neighbour mark variance index 
For marks of any type, there are the following:
Gmulti  multitype nearest neighbour distribution 
Kmulti  multitype Kfunction 
Jmulti  multitype Jfunction 
Alternatively use cut.ppp
to convert a marked point pattern
to a multitype point pattern.
Programming tools:
marktable  tabulate the marks of neighbours in a point pattern 
Summary statistics for a threedimensional point pattern:
These are for 3dimensional point pattern objects (class pp3
).
F3est  empty space function F 
G3est  nearest neighbour function G 
K3est  Kfunction 
pcf3est  pair correlation function 
Related facilities:
envelope.pp3  simulation envelopes 
Summary statistics for random sets:
These work for point patterns (class ppp
),
line segment patterns (class psp
)
or windows (class owin
).
Hest  spherical contact distribution H 
Gfox  Foxall Gfunction 
Jfox  Foxall Jfunction 
Model fitting (Cox and cluster models)
Cluster process models (with homogeneous or inhomogeneous intensity)
and Cox processes can be fitted by the function kppm
.
Its result is an object of class "kppm"
.
The fitted model can be printed, plotted, predicted, simulated
and updated.
kppm  Fit model 
plot.kppm  Plot the fitted model 
summary.kppm  Summarise the fitted model 
fitted.kppm  Compute fitted intensity 
predict.kppm  Compute fitted intensity 
update.kppm  Update the model 
improve.kppm  Refine the estimate of trend 
simulate.kppm  Generate simulated realisations 
vcov.kppm  Variancecovariance matrix of coefficients 
coef.kppm
 Extract trend coefficients 
formula.kppm
 Extract trend formula 
parameters  Extract all model parameters 
clusterfield  Compute offspring density 
clusterradius  Radius of support of offspring density 
Kmodel.kppm  K function of fitted model 
pcfmodel.kppm  Pair correlation of fitted model 
For model selection, you can also use
the generic functions step
, drop1
and AIC
on fitted point process models.
For variable selection, see sdr
.
The theoretical models can also be simulated,
for any choice of parameter values,
using rThomas
, rMatClust
,
rCauchy
, rVarGamma
,
and rLGCP
.
Lowerlevel fitting functions include:
lgcp.estK  fit a logGaussian Cox process model 
lgcp.estpcf  fit a logGaussian Cox process model 
thomas.estK  fit the Thomas process model 
thomas.estpcf  fit the Thomas process model 
matclust.estK  fit the \Matern Cluster process model 
matclust.estpcf  fit the \Matern Cluster process model 
cauchy.estK  fit a NeymanScott Cauchy cluster process 
cauchy.estpcf  fit a NeymanScott Cauchy cluster process 
vargamma.estK  fit a NeymanScott Variance Gamma process 
vargamma.estpcf  fit a NeymanScott Variance Gamma process 
mincontrast  lowlevel algorithm for fitting models 
by the method of minimum contrast 
Model fitting (Poisson and Gibbs models)
Poisson point processes are the simplest models for point patterns. A Poisson model assumes that the points are stochastically independent. It may allow the points to have a nonuniform spatial density. The special case of a Poisson process with a uniform spatial density is often called Complete Spatial Randomness.
Poisson point processes are included in the more general class of Gibbs point process models. In a Gibbs model, there is interaction or dependence between points. Many different types of interaction can be specified.
For a detailed explanation of how to fit Poisson or Gibbs point process models to point pattern data using spatstat, see Baddeley and Turner (2005b) or Baddeley (2008).
To fit a Poisson or Gibbs point process model:
Model fitting in spatstat is performed mainly by the function
ppm
. Its result is an object of class "ppm"
.
Here are some examples, where X
is a point pattern (class
"ppp"
):
command  model 
ppm(X)  Complete Spatial Randomness 
ppm(X ~ 1)  Complete Spatial Randomness 
ppm(X ~ x)  Poisson process with 
intensity loglinear in x coordinate  
ppm(X ~ 1, Strauss(0.1))  Stationary Strauss process 
ppm(X ~ x, Strauss(0.1))  Strauss process with 
conditional intensity loglinear in x 
It is also possible to fit models that depend on other covariates.
Manipulating the fitted model:
plot.ppm  Plot the fitted model 
predict.ppm
 Compute the spatial trend and conditional intensity 
of the fitted point process model  
coef.ppm  Extract the fitted model coefficients 
parameters  Extract all model parameters 
formula.ppm  Extract the trend formula 
intensity.ppm  Compute fitted intensity 
Kmodel.ppm  K function of fitted model 
pcfmodel.ppm  pair correlation of fitted model 
fitted.ppm  Compute fitted conditional intensity at quadrature points 
residuals.ppm  Compute point process residuals at quadrature points 
update.ppm  Update the fit 
vcov.ppm  Variancecovariance matrix of estimates 
rmh.ppm  Simulate from fitted model 
simulate.ppm  Simulate from fitted model 
print.ppm  Print basic information about a fitted model 
summary.ppm  Summarise a fitted model 
effectfun  Compute the fitted effect of one covariate 
logLik.ppm  loglikelihood or logpseudolikelihood 
anova.ppm  Analysis of deviance 
model.frame.ppm  Extract data frame used to fit model 
model.images  Extract spatial data used to fit model 
model.depends  Identify variables in the model 
as.interact  Interpoint interaction component of model 
fitin  Extract fitted interpoint interaction 
is.hybrid  Determine whether the model is a hybrid 
valid.ppm  Check the model is a valid point process 
project.ppm  Ensure the model is a valid point process 
For model selection, you can also use
the generic functions step
, drop1
and AIC
on fitted point process models.
For variable selection, see sdr
.
See spatstat.options
to control plotting of fitted model.
To specify a point process model:
The first order “trend” of the model is determined by an R language formula. The formula specifies the form of the logarithm of the trend.
X ~ 1  No trend (stationary) 
X ~ x  Loglinear trend lambda(x,y) = exp(alpha + beta * x) 
where x,y are Cartesian coordinates  
X ~ polynom(x,y,3)  Logcubic polynomial trend 
X ~ harmonic(x,y,2)  Logharmonic polynomial trend 
X ~ Z  Loglinear function of covariate Z 
lambda(x,y) = exp(alpha + beta * Z(x,y)) 
The higher order (“interaction”) components are described by
an object of class "interact"
. Such objects are created by:
Poisson()  the Poisson point process 
AreaInter()  Areainteraction process 
BadGey()  multiscale Geyer process 
Concom()  connected component interaction 
DiggleGratton()  DiggleGratton potential 
DiggleGatesStibbard()  DiggleGatesStibbard potential 
Fiksel()  Fiksel pairwise interaction process 
Geyer()  Geyer's saturation process 
Hardcore()  Hard core process 
HierHard()  Hierarchical multiype hard core process 
HierStrauss()  Hierarchical multiype Strauss process 
HierStraussHard()  Hierarchical multiype Strausshard core process 
Hybrid()  Hybrid of several interactions 
LennardJones()  LennardJones potential 
MultiHard()  multitype hard core process 
MultiStrauss()  multitype Strauss process 
MultiStraussHard()  multitype Strauss/hard core process 
OrdThresh()  Ord process, threshold potential 
Ord()  Ord model, usersupplied potential 
PairPiece()  pairwise interaction, piecewise constant 
Pairwise()  pairwise interaction, usersupplied potential 
Penttinen()  Penttinen pairwise interaction 
SatPiece()  Saturated pair model, piecewise constant potential 
Saturated()  Saturated pair model, usersupplied potential 
Softcore()  pairwise interaction, soft core potential 
Strauss()  Strauss process 
StraussHard()  Strauss/hard core point process 
Triplets()  Geyer triplets process 
Note that it is also possible to combine several such interactions
using Hybrid
.
Simulation and goodnessoffit for fitted models:
rmh.ppm  simulate realisations of a fitted model 
simulate.ppm  simulate realisations of a fitted model 
envelope  compute simulation envelopes for a fitted model 
Model fitting (determinantal point process models)
Code for fitting determinantal point process models has recently been added to spatstat.
For information, see the help file for dppm
.
Model fitting (spatial logistic regression)
Pixelbased spatial logistic regression is an alternative technique for analysing spatial point patterns that is widely used in Geographical Information Systems. It is approximately equivalent to fitting a Poisson point process model.
In pixelbased logistic regression, the spatial domain is divided into small pixels, the presence or absence of a data point in each pixel is recorded, and logistic regression is used to model the presence/absence indicators as a function of any covariates.
Facilities for performing spatial logistic regression are provided in spatstat for comparison purposes.
Fitting a spatial logistic regression
Spatial logistic regression is performed by the function
slrm
. Its result is an object of class "slrm"
.
There are many methods for this class, including methods for
print
, fitted
, predict
, simulate
,
anova
, coef
, logLik
, terms
,
update
, formula
and vcov
.
For example, if X
is a point pattern (class
"ppp"
):
command  model 
slrm(X ~ 1)  Complete Spatial Randomness 
slrm(X ~ x)  Poisson process with 
intensity loglinear in x coordinate  
slrm(X ~ Z)  Poisson process with 
intensity loglinear in covariate Z

Manipulating a fitted spatial logistic regression
anova.slrm  Analysis of deviance 
coef.slrm  Extract fitted coefficients 
vcov.slrm  Variancecovariance matrix of fitted coefficients 
fitted.slrm  Compute fitted probabilities or intensity 
logLik.slrm  Evaluate loglikelihood of fitted model 
plot.slrm  Plot fitted probabilities or intensity 
predict.slrm  Compute predicted probabilities or intensity with new data 
simulate.slrm  Simulate model 
There are many other undocumented methods for this class,
including methods for print
, update
, formula
and terms
. Stepwise model selection is
possible using step
or stepAIC
.
For variable selection, see sdr
.
Simulation
There are many ways to generate a random point pattern, line segment pattern, pixel image or tessellation in spatstat.
Random point patterns: Functions for random generation are now contained in the spatstat.random package.
See also varblock
for estimating the variance
of a summary statistic by block resampling, and
lohboot
for another bootstrap technique.
Fitted point process models:
If you have fitted a point process model to a point pattern dataset, the fitted model can be simulated.
Cluster process models
are fitted by the function kppm
yielding an
object of class "kppm"
. To generate one or more simulated
realisations of this fitted model, use
simulate.kppm
.
Gibbs point process models
are fitted by the function ppm
yielding an
object of class "ppm"
. To generate a simulated
realisation of this fitted model, use rmh.ppm
.
To generate one or more simulated realisations of the fitted model,
use simulate.ppm
.
Other random patterns: Functions for random generation are now contained in the spatstat.random package.
Simulationbased inference
envelope  critical envelope for Monte Carlo test of goodnessoffit 
bits.envelope  critical envelope for balanced twostage Monte Carlo test 
qqplot.ppm  diagnostic plot for interpoint interaction 
scan.test  spatial scan statistic/test 
studpermu.test  studentised permutation test 
segregation.test  test of segregation of types 
Hypothesis tests:
quadrat.test  chi^2 goodnessoffit test on quadrat counts 
clarkevans.test  Clark and Evans test 
cdf.test  Spatial distribution goodnessoffit test 
berman.test  Berman's goodnessoffit tests 
envelope  critical envelope for Monte Carlo test of goodnessoffit 
scan.test  spatial scan statistic/test 
dclf.test  DiggleCressieLoosmoreFord test 
mad.test  Mean Absolute Deviation test 
anova.ppm  Analysis of Deviance for point process models 
More recentlydeveloped tests:
dg.test  DaoGenton test 
bits.test  Balanced independent twostage test 
dclf.progress  Progress plot for DCLF test 
mad.progress  Progress plot for MAD test 
Sensitivity diagnostics:
Classical measures of model sensitivity such as leverage and influence have been adapted to point process models.
leverage.ppm  Leverage for point process model 
influence.ppm  Influence for point process model 
dfbetas.ppm  Parameter influence 
dffit.ppm  Effect change diagnostic 
Diagnostics for covariate effect:
Classical diagnostics for covariate effects have been adapted to point process models.
parres  Partial residual plot 
addvar  Added variable plot 
rhohat  Kernel estimate of covariate effect 
rho2hat  Kernel estimate of covariate effect (bivariate) 
Residual diagnostics:
Residuals for a fitted point process model, and diagnostic plots based on the residuals, were introduced in Baddeley et al (2005) and Baddeley, Rubak and \Moller (2011).
Type demo(diagnose)
for a demonstration of the diagnostics features.
diagnose.ppm  diagnostic plots for spatial trend 
qqplot.ppm  diagnostic QQ plot for interpoint interaction 
residualspaper  examples from Baddeley et al (2005) 
Kcom  model compensator of K function 
Gcom  model compensator of G function 
Kres  score residual of K function 
Gres  score residual of G function 
psst  pseudoscore residual of summary function 
psstA  pseudoscore residual of empty space function 
psstG  pseudoscore residual of G function 
compareFit  compare compensators of several fitted models 
Resampling and randomisation procedures
You can build your own tests based on randomisation and resampling using the following capabilities:
quadratresample  block resampling 
rshift  random shifting of (subsets of) points 
rthin  random thinning 
This library and its documentation are usable under the terms of the "GNU General Public License", a copy of which is distributed with the package.
Kasper Klitgaard Berthelsen, Ottmar Cronie, Tilman Davies, Julian Gilbey, Yongtao Guan, Ute Hahn, Kassel Hingee, Abdollah Jalilian, MarieColette van Lieshout, Greg McSwiggan, Tuomas Rajala, Suman Rakshit, Dominic Schuhmacher, Rasmus Waagepetersen and Hangsheng Wang made substantial contributions of code.
For comments, corrections, bug alerts and suggestions, we thank Monsuru Adepeju, Corey Anderson, Ang Qi Wei, Ryan Arellano, Jens Astrom, Robert Aue, Marcel Austenfeld, Sandro Azaele, Malissa Baddeley, Guy Bayegnak, Colin Beale, Melanie Bell, Thomas Bendtsen, Ricardo Bernhardt, Andrew Bevan, Brad Biggerstaff, Anders Bilgrau, Leanne Bischof, Christophe Biscio, Roger Bivand, Jose M. Blanco Moreno, Florent Bonneu, Jordan Brown, Ian Buller, Julian Burgos, Simon Byers, YaMei Chang, Jianbao Chen, Igor Chernayavsky, Y.C. Chin, Bjarke Christensen, Lucia Cobo Sanchez, JeanFrancois Coeurjolly, Kim Colyvas, Hadrien Commenges, Rochelle Constantine, Robin Corria Ainslie, Richard Cotton, Marcelino de la Cruz, Peter Dalgaard, Mario D'Antuono, Sourav Das, Peter Diggle, Patrick Donnelly, Ian Dryden, Stephen Eglen, Ahmed ElGabbas, Belarmain Fandohan, Olivier Flores, David Ford, Peter Forbes, Shane Frank, Janet Franklin, FunwiGabga Neba, Oscar Garcia, Agnes Gault, Jonas Geldmann, Marc Genton, Shaaban Ghalandarayeshi, Jason Goldstick, Pavel Grabarnik, C. Graf, Ute Hahn, Andrew Hardegen, Martin \Bogsted Hansen, Martin Hazelton, Juha Heikkinen, Mandy Hering, Markus Herrmann, Maximilian Hesselbarth, Paul Hewson, Hamidreza Heydarian, Kurt Hornik, Philipp Hunziker, Jack Hywood, Ross Ihaka, Cenk Icos, Aruna Jammalamadaka, Robert JohnChandran, Devin Johnson, Mahdieh Khanmohammadi, Bob Klaver, Lily KozmianLedward, Peter Kovesi, Mike Kuhn, Jeff Laake, Robert Lamb, Frederic Lavancier, Tom Lawrence, Tomas Lazauskas, Jonathan Lee, George Leser, Angela Li, Li Haitao, George Limitsios, Andrew Lister, Nestor Luambua, Ben Madin, Martin Maechler, Kiran Marchikanti, Jeff Marcus, Robert Mark, Peter McCullagh, Monia Mahling, Jorge Mateu Mahiques, Ulf Mehlig, Frederico Mestre, Sebastian Wastl Meyer, Mi Xiangcheng, Lore De Middeleer, Robin Milne, Enrique Miranda, Jesper \Moller, Annie Mollie, Ines Moncada, Mehdi Moradi, Virginia Morera Pujol, Erika Mudrak, Gopalan Nair, Nader Najari, Nicoletta Nava, Linda Stougaard Nielsen, Felipe Nunes, Jens Randel Nyengaard, Jens \Oehlschlaegel, Thierry Onkelinx, Sean O'Riordan, Evgeni Parilov, Jeff Picka, Nicolas Picard, Tim Pollington, Mike Porter, Sergiy Protsiv, Adrian Raftery, Ben Ramage, Pablo Ramon, Xavier Raynaud, Nicholas Read, Matt Reiter, Ian Renner, Tom Richardson, Brian Ripley, Ted Rosenbaum, Barry Rowlingson, Jason Rudokas, Tyler Rudolph, John Rudge, Christopher Ryan, Farzaneh Safavimanesh, Aila \Sarkka, Cody Schank, Katja Schladitz, Sebastian Schutte, Bryan Scott, Olivia Semboli, Francois Semecurbe, Vadim Shcherbakov, Shen Guochun, Shi Peijian, HaroldJeffrey Ship, Tammy L Silva, IdaMaria Sintorn, Yong Song, Malte Spiess, Mark Stevenson, Kaspar Stucki, Jan Sulavik, Michael Sumner, P. Surovy, Ben Taylor, Thordis Linda Thorarinsdottir, Leigh Torres, Berwin Turlach, Torben Tvedebrink, Kevin Ummer, Medha Uppala, Andrew van Burgel, Tobias Verbeke, Mikko Vihtakari, Alexendre Villers, Fabrice Vinatier, Maximilian Vogtland, Sasha Voss, Sven Wagner, Hao Wang, H. Wendrock, Jan Wild, Carl G. Witthoft, Selene Wong, Maxime Woringer, Luke Yates, Mike Zamboni and Achim Zeileis.
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